1-8 The detailed solution for the spreadsheet problem is available both on the instructor's

resource CD-ROM (in the file Solution for FM11 Ch 01 P08 Build a Model.xls) and on

the instructor's side of the textbook's web site, http://brigham.swcollege.com.

Answers and Solutions: 1- 11
MINI CASE

Assume that you recently graduated with a degree in finance and have just reported to
work as an investment advisor at the brokerage firm of Balik and Kiefer Inc. One of the
firm's clients is Michelle Dellatorre, a professional tennis player who has just come to the
United States from Chile. Dellatorre is a highly ranked tennis player who would like to
start a company to produce and market apparel that she designs. She also expects to
invest substantial amounts of money through Balik and Kiefer. Dellatorre is also very
bright, and, therefore, she would like to understand, in general terms, what will happen to
her money. Your boss has developed the following set of questions which you must ask
and answer to explain the U.S. financial system to Dellatorre.

2-26 The detailed solution for the spreadsheet problem is available both on the instructor's resource

CD-ROM (in the file Solution for Ch 02 P26 Build a Model.xls) and on the instructor's side of the

textbook's web site, brigham.swcollege.com.

Answers and Solutions: 2 - 40
MINI CASE

Assume that you are nearing graduation and that you have applied for a job with a local
bank. As part of the bank's evaluation process, you have been asked to take an
examination which covers several financial analysis techniques. The first section of the
test addresses discounted cash flow analysis. See how you would do by answering the
following questions.

a. Draw time lines for (a) a $100 lump sum cash flow at the end of year 2, (b) an ordinary

annuity of $100 per year for 3 years, and (c) an uneven cash flow stream of -$50, $100, $75,

c. We sometimes need to find how long it will take a sum of money (or anything else) to grow

to some specified amount. For example, if a company's sales are growing at a rate of 20

percent per year, how long will it take sales to double?

Answer: We have this situation in time line format:

0 1 2 3 3.8 4

20%

| | | | | |

-12 2

Say we want to find out how long it will take us to double our money at an interest rate of

20%. We can use any numbers, say $1 and $2, with this equation:

FVn = $2 = $1(1 + i)n = $1(1.20)n.

(1.2)n = $2/$1 = 2

n LN(1.2) = LN(2)

n = LN(2)/LN(1.2)

n = 0.693/0.182 = 3.8.

Answers and Solutions: 3- 43
Alternatively, we could use a financial calculator. We would plug I = 20, PV = -1, PMT = 0, and
FV = 2 into our calculator, and then press the N button to find the number of years it would take 1

(or any other beginning amount) to

FV
double when growth occurs at a 20%
rate. The answer is 3.8 years, but
some calculators will round this value 2

up to the next highest whole number.
The graph also shows what is
happening.

1

3.8

0 1 2 3 4

Year

Answers and Solutions: 3- 44
d. If you want an investment to double in three years, what interest rate must it earn?

This is slightly different from our earlier answer, because n is actually 273/365 = 0.7479
rather than 0.75.

Fractional time periods

Thus far all of our examples have dealt with full years. Now we are going to look at the
situation when we are dealing with fractional years, such as 9 months, or 10 years. In these
situations, proceed as follows:

· As always, start by drawing a time line so you can visualize the situation.

· Then think about the interest rate--the nominal rate, the compounding periods per

year, and the effective annual rate. If you have been given a nominal rate, you

may have to convert to the ear, using this formula:

m

i

EAR = 1 + Nom - 1 .

m

· If you have the effective annual rate--either because it was given to you or after

you calculated it with the formula--then you can find the PV of a lump sum by

applying this equation:

t

1

PV = FVt .

1 + EAR

· Here t can be a fraction of a year, such as 0.75, if you need to find the PV of

$1,000 due in 9 months, or 450/365 = 1.2328767 if the payment is due in 450

days.

· If you have an annuity with payments different from once a year, say every month,

you can always work it out as a series of lump sums. That procedure always

works. We can also use annuity formulas and calculator functions, but you have

to be careful.

Answers and Solutions: 3- 53
l. 1. What is the value at the end of year 3 of the following cash flow stream if the quoted interest

rate is 10 percent, compounded semiannually?

0 1 2 3
YEARS

| | | | | | |

100 100 100

Answer: 0 1 2

5%
3

| | | | | | |

100 100 100

110.25 = 100(1.05)2

121.55 = 100(1.05)4

331.80

Here we have a different situation. The payments occur annually, but compounding occurs each

6 months. Thus, we cannot use normal annuity valuation techniques. There are two

approaches that can be applied: (1) treat the cash flows as lump sums, as was done above, or (2)

treat the cash flows as an ordinary annuity, but use the effective annual rate:

m 2

0.10

EAR = 1 + i Nom - 1 = 1 + - 1 = 10.25%.

m 2

Now we have this 3-period annuity:

FVA3 = $100(1.1025)2 + $100(1.1025)1 + $100 = $331.80.

You can plug in n = 3, I = 10.25, PV = 0, and PMT = -100, and then press the FV button to find

FV = $331.80.

l. 2. What is the PV of the same stream?

Answer: 0 1 2
3 5%

| | | | | | |

100 100 100

90.70

82.27 PV = 100(1.05)-4

74.62

247.59

PV = $100(2.4759) = $247.59 AT 10.25%.

To use a financial calculator, input N = 3, I = 10.25, PMT = 100, FV = 0, and then press the PV

key to find PV = $247.59.

Answers and Solutions: 3- 54
l. 3. Is the stream an annuity?

Answer: The payment stream is an annuity in the sense of constant amounts at regular intervals, but the

intervals do not correspond with the compounding periods. This kind of situation occurs often.

In this situation the interest is compounded semiannually, so with a quoted rate of 10%, the ear

will be 10.25%. Here we could find the effective rate and then treat it as an annuity. Enter N =

3, I = 10.25, PMT = 100, and FV = 0. Now press PV to get $247.59.

l. 4. An important rule is that you should never show a nominal rate on a time line or use it in

Donna Jamison, a recent graduate of the University of Tennessee with four years of
banking experience, was recently brought in as assistant to the chairman of the board of
Computron Industries, a manufacturer of electronic calculators.

The company doubled its plant capacity, opened new sales offices outside its home
territory, and launched an expensive advertising campaign. Computron's results were
not satisfactory, to put it mildly. Its board of directors, which consisted of its president
and vice-president plus its major stockholders (who were all local business people), was
most upset when directors learned how the expansion was going. Suppliers were being
paid late and were unhappy, and the bank was complaining about the deteriorating
situation and threatening to cut off credit. As a result, Al Watkins, Computron's
president, was informed that changes would have to be made, and quickly, or he would be
fired. Also, at the board's insistence Donna Jamison was brought in and given the job of
assistant to Fred Campo, a retired banker who was Computron's chairman and largest
stockholder. Campo agreed to give up a few of his golfing days and to help nurse the
company back to health, with Jamison's help.

Jamison began by gathering financial statements and other data. Assume that you are
Jamison's assistant, and you must help her answer the following questions for Campo.

2. bi excluding the stock with the beta equal to 1.0 is 22.4 - 1.0 = 21.4, so the beta of the portfolio

excluding this stock is b = 21.4/19 = 1.1263. The beta of the new portfolio is:

1.1263(0.95) + 1.75(0.05) = 1.1575 = 1.16.

$400,000 $600,000
4-9 Portfolio beta = (1.50) + (-0.50)

$4,000,000 $4,000,000

$1,000,000 $2,000,000

+ (1.25) + (0.75)

$4,000,000 $4,000,000

= 0.1)(1.5) + (0.15)(-0.50) + (0.25)(1.25) + (0.5)(0.75)

= 0.15 - 0.075 + 0.3125 + 0.375 = 0.7625.

rp = rRF + (rM - rRF)(bp) = 6% + (14% - 6%)(0.7625) = 12.1%.

Answers and Solutions: 4 - 77
Alternative solution: First compute the return for each stock using the CAPM equation [rRF + (rM -

rRF)b], and then compute the weighted average of these returns.

rRF = 6% and rM - rRF = 8%.

Stock Investment Beta r = rRF + (rM - rRF)b Weight

A $ 400,000 1.50 18%
0.10

B 600,000 (0.50) 2
0.15

C 1,000,000 1.25 16
0.25

D 2,000,000 0.75 12
0.50

Total $4,000,000
1.00

rp = 18%(0.10) + 2%(0.15) + 16%(0.25) + 12%(0.50) = 12.1%.

4-10 First, calculate the beta of what remains after selling the stock:

bp = 1.1 = ($100,000/$2,000,000)0.9 + ($1,900,000/$2,000,000)bR

1.1 = 0.045 + (0.95)bR

bR = 1.1105.

bN = (0.95)1.1105 + (0.05)1.4 = 1.125.

4-11 We know that bR = 1.50, bS = 0.75, rM = 13%, rRF = 7%.

ri = rRF + (rM - rRF)bi = 7% + (13% - 7%)bi.

rR = 7% + 6%(1.50) = 16.0%

rS = 7% + 6%(0.75) = 11.5

4.5%

4-12 The answers to a, b, c, and d are given below:

rA rB Portfolio

2000 (18.00%) (14.50%) (16.25%)

2001 33.00 21.80

27.40

2002 15.00 30.50

22.75

2003 (0.50) (7.60)

(4.05)

Answers and Solutions: 4 - 78
2004 27.00 26.30

26.65

Mean 11.30 11.30

11.30

Std Dev 20.79 20.78

20.13

CV 1.84 1.84

1.78

e. A risk-averse investor would choose the portfolio over either Stock A or Stock B alone, since the

portfolio offers the same expected return but with less risk. This result occurs because returns on

A and B are not perfectly positively correlated (AB = 0.88).

4-13 a. bX = 1.3471; bY = 0.6508.

b. rX = 6% + (5%)1.3471 = 12.7355%.

rY = 6% + (5%)0.6508 = 9.2540%.

c. bp = 0.8(1.3471) + 0.2(0.6508) = 1.2078.

rp = 6% + (5%)1.2078 = 12.04%.

Alternatively,

rp = 0.8(12.7355%) + 0.2(9.254%) = 12.04%.

d. Stock X is undervalued, because its expected return exceeds its required rate of return.

Answers and Solutions: 4 - 79
SOLUTION TO SPREADSHEET PROBLEM

4-14 The detailed solution for the spreadsheet problem is available both on the instructor's resource

CD-ROM (in the file Solution for FM11 Ch 04 P14 Build a Model.xls) and on the instructor's side of

the textbook's web site, brigham.swcollege.com.

Answers and Solutions: 4 - 80
MINI CASE

Assume that you recently graduated with a major in finance, and you just landed a job as a
financial planner with Barney Smith Inc., a large financial services corporation. Your
first assignment is to invest $100,000 for a client. Because the funds are to be invested in a
business at the end of one year, you have been instructed to plan for a one-year holding
period. Further, your boss has restricted you to the following investment alternatives,
shown with their probabilities and associated outcomes. (Disregard for now the items at the
bottom of the data; you will fill in the blanks later.)

Returns On Alternative Investments

Estimated Rate Of Return

State of the T- Alta Repo Am.

Market 2-stock

economy prob. Bills Inds Men Foam portfolio portfolio

Recession 0.1 8.0% -22.0% 28.0% 10.0%* -13.0% 3.0%

Below avg 0.2 8.0 -2.0 14.7 -10.0 1.0

Average 0.4 8.0 20.0 0.0 7.0 15.0 10.0

Above avg 0.2 8.0 35.0 -10.0 45.0 29.0

Boom 0.1 8.0 50.0 -20.0 30.0 43.0 15.0

r-hat ( r ) 1.7% 13.8% 15.0%

Std dev () 0.0 13.4 18.8 15.3

Coef of var (cv) 7.9 1.4 1.0

beta (b) -0.86 0.68

*Note that the estimated returns of American Foam do not always move in the same
direction as the overall economy. For example, when the economy is below average,
consumers purchase fewer mattresses than they would if the economy was stronger.
However, if the economy is in a flat-out recession, a large number of consumers who were
planning to purchase a more expensive inner spring mattress may purchase, instead, a
cheaper foam mattress. Under these circumstances, we would expect American Foam's
stock price to be higher if there is a recession than if the economy was just below average.

Barney Smith's economic forecasting staff has developed probability estimates for the
state of the economy, and its security analysts have developed a sophisticated computer
program which was used to estimate the rate of return on each alternative under each state
of the economy. Alta Industries is an electronics firm; Repo Men collects past-due debts;
and American Foam manufactures mattresses and other foam products. Barney Smith
also maintains an "index fund" which owns a market-weighted fraction of all publicly
traded stocks; you can invest in that fund, and thus obtain average stock market results.
Given the situation as described, answer the following questions.

Answers and Solutions: 5 - 81
a. What are investment returns? What is the return on an investment that costs

$1,000 and is sold after one year for $1,100?

Answer: Investment return measures the financial results of an investment. They may be expressed in

r RF remains at 8 percent, but now r M increases to 18 percent, so the market risk premium

increases to 10 percent. The required rate of return will rise sharply on high-risk (high-beta)

stocks, but not much on low-beta securities.

Answers and Solutions: 5 - 94
Optional question (cover if time is available)

Financial managers are more concerned with investment decisions relating to real assets
such as plant and equipment than with investments in financial assets such as securities.
How does the analysis that we have gone through relate to real asset investment decisions,
especially corporate capital budgeting decisions?

Answer: There is a great deal of similarity between your financial asset decisions and a firm's capital

budgeting decisions. Here is the linkage:

1. A company may be thought of as a portfolio of assets. If the company diversifies its assets,

and especially if it invests in some projects that tend to do well when others are doing badly,

it can lower the variability of its returns.

2. Companies obtain their investment funds from investors, who buy the firm's

stocks and bonds. When investors buy these securities, they require a risk

premium which is based on the company's risk as they (investors) see it. Further,

since investors in general hold well-diversified portfolios of stocks and bonds, the

risk that is relevant to them is the security's market risk, not its stand-alone risk.

Thus, investors view the risk of the firm from a market risk perspective.

3. Therefore, when a manager makes a decision to build a new plant, the riskiness of

the investment in the plant that is relevant to the firm's investors (its owners) is its

market risk, not its stand-alone risk. Accordingly, managers need to know how

Sam Strother and Shawna Tibbs are vice-presidents of Mutual of Seattle Insurance
Company and co-directors of the company's pension fund management division. A major
new client, the Northwestern Municipal Alliance, has requested that Mutual of Seattle
present an investment seminar to the mayors of the represented cities, and Strother and
Tibbs, who will make the actual presentation, have asked you to help them by answering
the following questions. Because the Boeing Company operates in one of the league's
cities, you are to work Boeing into the presentation.

a. What are the key features of a bond?

Answer:

1. Par or face value. We generally assume a $1,000 par value, but par can be anything, and

often $5,000 or more is used. With registered bonds, which is what are issued today, if you

bought $50,000 worth, that amount would appear on the certificate.

2. Coupon rate. The dollar coupon is the "rent" on the money borrowed, which is generally the

par value of the bond. The coupon rate is the annual interest payment divided by the par

value, and it is generally set at the value of r on the day the bond is issued.

3. Maturity. This is the number of years until the bond matures and the issuer must repay the

loan (return the par value).

4. Issue date. This is the date the bonds were issued.

5. Default risk is inherent in all bonds except treasury bonds--will the issuer have the cash to

make the promised payments? Bonds are rated from AAA to D, and the lower the rating the

riskier the bond, the higher its default risk premium, and, consequently, the higher its required

rate of return, r.

Answers and Solutions: 7 - 125
b. What are call provisions and sinking fund provisions? Do these provisions make bonds

more or less risky?

Answer: A call provision is a provision in a bond contract that gives the issuing corporation the right to

redeem the bonds under specified terms prior to the normal maturity date. The call provision

generally states that the company must pay the bondholders an amount greater than the par value

if they are called. The additional sum, which is called a call premium, is typically set equal to

one year's interest if the bonds are called during the first year, and the premium declines at a

constant rate of INT/n each year thereafter.

A sinking fund provision is a provision in a bond contract that requires the issuer to retire a

portion of the bond issue each year. A sinking fund provision facilitates the orderly retirement of

the bond issue.

The call privilege is valuable to the firm but potentially detrimental to the investor, especially

if the bonds were issued in a period when interest rates were cyclically high. Therefore, bonds

with a call provision are riskier than those without a call provision. Accordingly, the interest rate

on a new issue of callable bonds will exceed that on a new issue of noncallable bonds.

Although sinking funds are designed to protect bondholders by ensuring that an issue is

retired in an orderly fashion, it must be recognized that sinking funds will at times work to the

detriment of bondholders. On balance, however, bonds that provide for a sinking fund are

regarded as being safer than those without such a provision, so at the time they are issued sinking

fund bonds have lower coupon rates than otherwise similar bonds without sinking funds.

Answers and Solutions: 7 - 126
c. How is the value of any asset whose value is based on expected future cash flows

determined?

Answer: 0 1 2 3
n

| | | | ··· |

CF1 CF2 CF3
CFn

PV CF1

PV CF2

The value of an asset is merely the present value of its expected future cash flows:

n

VALUE = PV =

CF1

1

+

CF2

(1 + r ) (1 + r ) 2

+

CF3

(1 + r ) 3

+ ... +

CFn

(1 + r ) n

= CFt

t = 1 (1 + r )

t

.

If the cash flows have widely varying risk, or if the yield curve is not horizontal, which signifies

that interest rates are expected to change over the life of the cash flows, it would be logical for

each period's cash flow to have a different discount rate. However, it is very difficult to make

such adjustments; hence it is common practice to use a single discount rate for all cash flows.

The discount rate is the opportunity cost of capital; that is, it is the rate of return that could be

obtained on alternative investments of similar risk. Thus, the discount rate depends primarily on

factors discussed back in chapter 1:

ri = r* + IP + LP + MRP + DRP.

Answers and Solutions: 7 - 127
d. How is the value of a bond determined? What is the value of a 10-year, $1,000 par

value bond with a 10 percent annual coupon if its required rate of return is 10

percent?

Answer: A bond has a specific cash flow pattern consisting of a stream of constant interest payments plus

the return of par at maturity. The annual coupon payment is the cash flow: pmt = (coupon rate)

× (par value) = 0.1($1,000) = $100.

For a 10-year, 10 percent annual coupon bond, the bond's value is found as follows:

0 1 2 3 9

10%

10

| | | | ··· | |

100 100 100 100 100

90.91 + 1,000

82.64

.

.

.

38.55

385.54

1,000.00

Expressed as an equation, we have:

$100 $100 $1,000

VB = 1

+ ... + 10

+

(1 + r ) (1 + r ) (1 + r )10

= $90.91 + . . . + $38.55 + $385.54 = $1,000.

or:

VB = $100(PVIFA10%,10) + $1,000(PVIF10%,10)

= $100 ((1-1/(1+.1)10)/0.10)+ $1,000 (1/(1+0.10)10).

The bond consists of a 10-year, 10% annuity of $100 per year plus a $1,000 lump sum payment at

t = 10:

PV Annuity = $ 614.46

PV Maturity Value = 385.54

Value Of Bond = $1,000.00

The mathematics of bond valuation is programmed into financial calculators which do the

operation in one step, so the easy way to solve bond valuation problems is with a financial

investors must pay taxes each year on the dividends received during the year, while taxes on

capital gains can be delayed until the gain is actually realized.

7-19 a. rs = rRF + (rM - rRF)b = 11% + (14% - 11%)1.5 = 15.5%.

^

P0 = D1/(rs - g) = $2.25/(0.155 - 0.05) = $21.43.

b. rs = 9% + (12% - 9%)1.5 = 13.5%. ^

P0 = $2.25/(0.135 - 0.05) = $26.47.

c. rs = 9% + (11% - 9%)1.5 = 12.0%. ^

P0 = $2.25/(0.12 - 0.05) = $32.14.

d. New data given: rRF = 9%; rM = 11%; g = 6%, b = 1.3.

rs = rRF + (rM - rRF)b = 9% + (11% - 9%)1.3 = 11.6%.

^

P0 = D1/(rs - g) = $2.27/(0.116 - 0.06) = $40.54.

Answers and Solutions: 7 - 153
SOLUTION TO SPREADSHEET PROBLEM

7-20 The detailed solution for the problem is available both on the instructor's resource CD-ROM (in the

file Solution for FM11 Ch 07 P20 Build a Model.xls) and on the instructor's side of the web site,

brigham.swcollege.com.

Answers and Solutions: 7 - 154
MINI CASE

Sam Strother and Shawna Tibbs are senior vice presidents of the Mutual of Seattle. They are
co-directors of the company's pension fund management division, with Strother having
responsibility for fixed income securities (primarily bonds) and Tibbs being responsible for
equity investments. A major new client, the Northwestern Municipal League, has requested
that Mutual of Seattle present an investment seminar to the mayors of the represented cities, and
Strother and Tibbs, who will make the actual presentation, have asked you to help them.

To illustrate the common stock valuation process, Strother and Tibbs have asked
you to analyze the Temp Force Company, an employment agency that supplies word
processor operators and computer programmers to businesses with temporarily heavy
workloads. You are to answer the following questions.

a. Describe briefly the legal rights and privileges of common stockholders.

Answer: The common stockholders are the owners of a corporation, and as such, they have certain rights

and privileges as described below.

1. Ownership implies control. Thus, a firm's common stockholders have the right to

elect its firm's directors, who in turn elect the officers who manage the business.

2. Common stockholders often have the right, called the preemptive right, to purchase

any additional shares sold by the firm. In some states, the preemptive right is

automatically included in every corporate charter; in others, it is necessary to insert it

specifically into the charter.

b. 1. Write out a formula that can be used to value any stock, regardless of its dividend

pattern.

Answer: The value of any stock is the present value of its expected dividend stream:

^ D1 D2 D3 D

P0 = + + + + .

(1 + rs ) t

(1 + rs ) (1 + rs ) 3

(1 + rs )

However, some stocks have dividend growth patterns which allow them to be valued using

short-cut formulas.

Answers and Solutions: 8 - 155
b. 2. What is a constant growth stock? How are constant growth stocks valued?

Answer: A constant growth stock is one whose dividends are expected to grow at a constant rate forever.

"Constant growth" means that the best estimate of the future growth rate is some constant number,

not that we really expect growth to be the same each and every year. Many companies have

dividends which are expected to grow steadily into the foreseeable future, and such companies are

valued as constant growth stocks.

For a constant growth stock:

D1 = D0(1 + g), D2 = D1(1 + g) = D0(1 + g)2, and so on.

With this regular dividend pattern, the general stock valuation model can be simplified to

the following very important equation:

^ D1 D 0 (1 + g )

P0 = = .

rs - g rs - g

This is the well-known "Gordon," or "constant-growth" model for valuing stocks. Here D1, is

the next expected dividend, which is assumed to be paid 1 year from now, rs is the required rate of

return on the stock, and g is the constant growth rate.

b. 3. What happens if a company has a constant g which exceeds its rs? Will many stocks have

expected g > rs in the short run (i.e., for the next few years)? In the long run (i.e., forever)?

Answer: The model is derived mathematically, and the derivation requires that rs > g. If g is greater than rs,

the model gives a negative stock price, which is nonsensical. The model simply cannot be used

unless (1) rs > g, (2) g is expected to be constant, and (3) g can reasonably be expected to continue

indefinitely.

Stocks may have periods of supernormal growth, where gs > rs; however, this growth rate

cannot be sustained indefinitely. In the long-run, g < rs.

c. Assume that temp force has a beta coefficient of 1.2, that the risk-free rate (the yield

on T-bonds) is 7 percent, and that the market risk premium is 5 percent. What is the

required rate of return on the firm's stock?

Answer: Here we use the SML to calculate temp force's required rate of return:

rs = rRF + (rM ­ rRF)bTemp Force = 7% + (12% - 7%)(1.2)

= 7% + (5%)(1.2) = 7% + 6% = 13%.

Answers and Solutions: 8 - 156
d. Assume that Temp Force is a constant growth company whose last dividend (D0, which was

paid yesterday) was $2.00, and whose dividend is expected to grow indefinitely at a 6 percent

rate.

d. 1. What is the firm's expected dividend stream over the next 3 years?

Answer: Temp Force is a constant growth stock, and its dividend is expected to grow at a constant rate of 6

percent per year. Expressed as a time line, we have the following setup. Just enter 2 in your

calculator; then keep multiplying by 1 + g = 1.06 to get D1, D2, and D3:

0 rs = 13% 1 2

3 4

| | | | |

g = 6%

D0 = 2.00 2.12 2.247 2.382

1.88

1.76

1.65

.

.

.

d. 2. What is the firm's current stock price?

Answer: We could extend the time line on out forever, find the value of Temp Force's dividends for every

year on out into the future, and then the PV of each dividend, discounted at r = 13%. For

example, the PV of D1 is $1.76106; the PV of D2 is $1.75973; and so forth. Note that the

dividend payments increase with time, but as long as rs > g, the present values decrease with time.

If we extended the graph on out forever and then summed the PVs of the dividends, we would

have the value of the stock. However, since the stock is growing at a constant rate, its value can

be estimated using the constant growth model:

^ D1 $2.12 $2.12

P0 = = = = $30.29.

rs - g 0.13 - 0.06 0.07

d. 3. What is the stock's expected value one

year from now?

Answer: After one year, D1 will have been paid, so the expected dividend stream will then be D2, D3, D4,

and so on. Thus, the expected value one year from now is $32.10:

^ D2 $2.247 $2.247

P1 = = = = $32.10.

( rs - g) (0.13 - 0.06) 0.07

Answers and Solutions: 8 - 157
d. 4. What are the expected dividend yield, the capital gains yield, and the total return

during the first year?

Answer: The expected dividend yield in any year n is

Dn

Dividend Yield = ,

^

P n -1

While the expected capital gains yield is

^ ^

( Pn - Pn -1 ) Dn

Capital Gains Yield = =r- .

^

Pn -1 Pn -1

Thus, the dividend yield in the first year is 10 percent, while the capital gains yield is 6

percent:

Total return = 13.0%

Dividend yield = $2.12/$30.29 = 7.0%

Capital gains yield = 6.0%

e. Now assume that the stock is currently selling at $30.29. What is the expected

rate of return on the stock?

Answer: The constant growth model can be rearranged to this form:

D1

r s= +g.

P0

Here the current price of the stock is known, and we solve for the expected return. For

Temp Force:

r s= $2.12/$30.29 + 0.060 = 0.070 + 0.060 = 13%.

Answers and Solutions: 8 - 158
f. What would the stock price be if its dividends were expected to have zero growth?

Answer: If Temp Force's dividends were not expected to grow at all, then its dividend

stream would be a perpetuity. Perpetuities are valued as shown below:

0 rs = 13% 1 2 3

| | | |

g = 0%

2.00 2.00 2.00

1.77

1.57

1.39

.

.

.

P0 = 15.38

P0 = PMT/r = $2.00/0.13 = $15.38.

Note that if a preferred stock is a perpetuity, it may be valued with this formula.

Answers and Solutions: 8 - 159
g. Now assume that Temp Force is expected to experience supernormal growth of 30

percent for the next 3 years, then to return to its long-run constant growth rate of 6

percent. What is the stock's value under these conditions? What is its expected

dividend yield and capital gains yield be in year 1? In year 4?

Answer: Temp Force is no longer a constant growth stock, so the constant growth model is not applicable.

Note, however, that the stock is expected to become a constant growth stock in 3 years. Thus, it

has a nonconstant growth period followed by constant growth. The easiest way to value such

nonconstant growth stocks is to set the situation up on a time line as shown below:

0r = 13% 1 2

s

3 4

| | | | |

g = 30% g = 30% g = 30% g = 6%

2.600 3.380 4.394

4.658

2.301

2.647

3.045

^ 4.658

46.116 P3 = $66.54 =

54.109 0.13 - 0.06

Simply enter $2 and multiply by (1.30) to get D1 = $2.60; multiply that result by 1.3 to get D2 =

$3.38, and so forth. Then recognize that after year 3, Temp Force becomes a constant growth

^ ^

stock, and at that point P3 can be found using the constant growth model. P3 is the present

value as of t = 3 of the dividends in year 4 and beyond.

^

With the cash flows for D1, D2, D3, and P3 shown on the time line, we discount each value

back to year 0, and the sum of these four PVs is the value of the stock today, P0 = $54.109.

The dividend yield in year 1 is 4.80 percent, and the capital gains yield is 8.2

percent:

$2.600

Dividend yield = = 0.0480 = 4.8%.

$54.109

Capital gains yield = 13.00% - 4.8% = 8.2%.

During the nonconstant growth period, the dividend yields and capital gains yields are not

constant, and the capital gains yield does not equal g. However, after year 3, the stock becomes

The option price is the current value of the stock in the portfolio minus the PV of the payoff:

V = 0.8($15) - $10.093 = $1.907 .$1.91.

8-6 Put = V ­ P + X exp(-rRF t)

= $6.56 - $33 + $32 e-0.06(1)

= $6.56 - $33 + $30.136 = $3.696 $3.70.

Answers and Solutions: 8 - 167
SOLUTION TO SPREADSHEET PROBLEMS

8-7 The detailed solution for the problem is available both on the instructor's resource CD-ROM (in the

file Solution for FM 11 Ch 08 P07 Build a Model.xls) and on the instructor's side of the textbook's

web site, http://brigham.swcollege.com.

Answers and Solutions: 8 - 168
MINI CASE

Assume that you have just been hired as a financial analyst by Triple Trice Inc., a mid-sized
California company that specializes in creating exotic clothing. Since no one at Triple Trice is
familiar with the basics of financial options, you have been asked to prepare a brief report that
the firm's executives could use to gain at least a cursory understanding of the topic.

To begin, you gathered some outside materials the subject and used these materials to draft a list of
pertinent questions that need to be answered. In fact, one possible approach to the paper is to use a
question-and-answer format. Now that the questions have been drafted, you have to develop the answers.

a. What is a financial option? What is the single most important characteristic of an

option?

Answer: A financial option is a contract which gives its holder the right to buy (or sell) an asset at a

predetermined price within a specified period of time. An option's most important characteristic

is that it does not obligate its owner to take any action; it merely gives the owner the right to buy

or sell an asset.

b. Options have a unique set of terminology. Define the following terms: (1) call

The total market value of the long-term debt is 30,000($659.46) = $19,783,800.

There are 1 million shares of stock outstanding, and the stock sells for $60 per share. Therefore,

the market value of the equity is $60,000,000.

The market value capital structure is thus:

Short-term debt $10,000,000 11.14%

Long-term debt 19,783,800 22.03

Common equity 60,000,000 66.83

$89,783,800 100.00%

Answers and Solutions: 9- 179
9-13 Several steps are involved in the solution of this problem. Our solution follows:

Step 1.

Establish a set of market value capital structure weights. In this case, A/P and accruals, and also

short-term debt, may be disregarded because the firm does not use these as a source of permanent

financing.

Debt:

The long-term debt has a market value found as follows:

40

$40 $1,000

V0 = t

+ = $699,

t =1 (1.06) (1.06) 40

or 0.699($30,000,000) = $20,970,000 in total.

Preferred Stock:

The preferred has a value of

$2

Pps = = $72.73.

0.11 / 4

There are $5,000,000/$100 = 50,000 shares of preferred outstanding, so the total market value of the

preferred is

50,000($72.73) = $3,636,500.

Common Stock:

The market value of the common stock is

4,000,000($20) = $80,000,000.

Therefore, here is the firm's market value capital structure, which we assume to be optimal:

Long-term debt $ 20,970,000 20.05%

Preferred stock 3,636,500 3.48

Common equity 80,000,000 76.47

$104,606,500 100.00%

We would round these weights to 20 percent debt, 4 percent preferred, and 76 percent common equity.

Step 2.

Establish cost rates for the various capital structure components.

Debt cost:

rd(1 - T) = 12%(0.6) = 7.2%.

Answers and Solutions: 9- 180
Preferred cost:

Annual dividend on new preferred = 11%($100) = $11. Therefore,

rps = $11/$100(1 - 0.05) = $11/$95 = 11.6%.

Common equity cost:

There are three basic ways of estimating rs: CAPM, DCF, and risk premium over own bonds. None
of the methods is very exact.

CAPM:

We would use rRF = T-bond rate = 10%. For RPM, we would use 4.5% to 5.5%. For beta, we would
use a beta in the 1.3 to 1.7 range. Combining these values, we obtain this range of values for rs:

Highest: rs = 10% + (5.5)(1.7) = 19.35%.

Lowest: rs = 10% + (4.5)(1.3) = 15.85%.

Midpoint: rs = 10% + (5.0)(1.5) = 17.50%.

DCE:

The company seems to be in a rapid, nonconstant growth situation, but we do not have the inputs
necessary to develop a nonconstant rs. Therefore, we will use the constant growth model but temper
our growth rate; that is, think of it as a long-term average g that may well be higher in the immediate
than in the more distant future.

Data exist that would permit us to calculate historic growth rates, but problems would clearly
arise, because the growth rate has been variable and also because gEPS gDPS. For the problem at
hand, we would simply disregard historic growth rates, except for a discussion about calculating them
as an exercise.

We could use as a growth estimator this method:

g = b(r) = 0.5(24%) = 12%.

It would not be appropriate to base g on the 30% ROE, because investors do not expect that rate.

Finally, we could use the analysts' forecasted g range, 10 to 15 percent. The dividend yield is
D1/P0. Assuming g = 12%,

D1 $1(1.12)

= = 5.6%.

P0 $20

One could look at a range of yields, based on P in the range of $17 to $23, but because we believe
in efficient markets, we would use P0 = $20. Thus, the DCF model suggests a rs in the range of 15.6 to
20.6 percent:

Highest: rs = 5.6% + 15% = 20.6%.

Lowest: rs = 5.6% + 10% = 15.6%.

Midpoint: rs = 5.6% + 12.5% = 18.1%.

Answers and Solutions: 9- 181
Generalized risk premium.

Highest: rs = 12% + 6% = 18%.

Lowest: rs = 12% + 4% = 16%.

Midpoint: rs = 12% + 5% = 17%.

Based on the three midpoint estimates, we have rs in this range:

CAPM 17.5%

DCF 18.1%

Risk Premium 17.0%

Step 3.

Calculate the WACC:

WACC = (D/V)(rdAT) + (P/V)(rps) + (S/V)(rs or re)

= 0.20(rdAT) + 0.04(rps) + 0.76(rs or re).

It would be appropriate to calculate a range of WACCs based on the ranges of component costs, but to

FV = -1000, to get I = 5.57%, which is the after-tax component cost of debt.

Answers and Solutions: 9- 182
SPREADSHEET PROBLEM

9-16 The detailed solution for the problem is available both on the instructor's resource CD-ROM (in the

file Solution for FM11 Ch 09 P16 Build a Model.xls) and on the instructor's side of the web site,

http://brigham.swcollege.com.

Answers and Solutions: 9- 183
MINI CASE

During the last few years, Harry Davis Industries has been too constrained by the high cost
of capital to make many capital investments. Recently, though, capital costs have been
declining, and the company has decided to look seriously at a major expansion program
that had been proposed by the marketing department. Assume that you are an assistant to
Leigh Jones, the financial vice-president. Your first task is to estimate Harry Davis' cost of
capital. Jones has provided you with the following data, which she believes may be
relevant to your task:

b. No. Salvage possibilities could only raise NPV and IRR. The value of the firm is maximized

by terminating the project after Year 3.

Answers and Solutions: 10 - 214
SOLUTION TO SPREADSHEET PROBLEM

10-18 The detailed solution for the problem is available both on the instructor's resource CD-ROM (in the

file Solution for FM11 Ch 10 P18 Build a Model.xls) and on the instructor's side of the web site,

brigham.swcollege.com.

Answers and Solutions: 10 - 215
MINI CASE

You have just graduated from the MBA program of a large university, and one of your
favorite courses was "Today's Entrepreneurs." In fact, you enjoyed it so much you have
decided you want to "be your own boss." While you were in the master's program, your
grandfather died and left you $300,000 to do with as you please. You are not an inventor
and you do not have a trade skill that you can market; however, you have decided that you
would like to purchase at least one established franchise in the fast foods area, maybe two
(if profitable). The problem is that you have never been one to stay with any project for
too long, so you figure that your time frame is three years. After three years you will sell
off your investment and go on to something else.

You have narrowed your selection down to two choices; (1) Franchise L: Lisa's Soups,
Salads, & Stuff and (2) Franchise S: Sam's Wonderful Fried Chicken. The net cash flows
shown below include the price you would receive for selling the franchise in year 3 and the
forecast of how each franchise will do over the three-year period. Franchise L's cash flows
will start off slowly but will increase rather quickly as people become more health
conscious, while Franchise S's cash flows will start off high but will trail off as other
chicken competitors enter the marketplace and as people become more health conscious
and avoid fried foods. Franchise L serves breakfast and lunch, while franchise S serves
only dinner, so it is possible for you to invest in both franchises. You see these franchises
as perfect complements to one another: you could attract both the lunch and dinner crowds
and the health conscious and not so health conscious crowds with the franchises directly
competing against one another.

Here are the projects' net cash flows (in thousands of dollars):

Expected Net Cash Flow

Year Franchise L Franchise S

0 ($100) ($100)

1 10 70

2 60 50

3 80 20

Depreciation, salvage values, net working capital requirements, and tax effects are all included in these
cash flows.

You also have made subjective risk assessments of each franchise, and concluded that both
franchises have risk characteristics that require a return of 10 percent. You must now determine
whether one or both of the projects should be accepted.

Answers and Solutions: 11 - 216
a. What is capital budgeting?

Answer: Capital budgeting is the process of analyzing additions to fixed assets. Capital budgeting is

important because, more than anything else, fixed asset investment decisions chart a company's

course for the future. Conceptually, the capital budgeting process is identical to the decision

process used by individuals making investment decisions. These steps are involved:

1. Estimate the cash flows--interest and maturity value or dividends in the case of bonds and

stocks, operating cash flows in the case of capital projects.

2. Assess the riskiness of the cash flows.

3. Determine the appropriate discount rate, based on the riskiness of the cash flows and the

general level of interest rates. This is called the project cost of capital in capital budgeting.

4. Evaluate the cash flows.

b. What is the difference between independent and mutually exclusive projects?

Answer: Projects are independent if the cash flows of one are not affected by the acceptance of the other.

Conversely, two projects are mutually exclusive if acceptance of one impacts adversely the cash

flows of the other; that is, at most one of two or more such projects may be accepted. Put

another way, when projects are mutually exclusive it means that they do the same job. For

example, a forklift truck versus a conveyor system to move materials, or a bridge versus a ferry

boat.

Projects with normal cash flows have outflows, or costs, in the first year (or years) followed

by a series of inflows. Projects with nonnormal cash flows have one or more outflows after the

inflow stream has begun. Here are some examples:

Inflow (+) Or Outflow (-) In Year

0 1 2 3 4 5

Normal - + + + + +

- - + + + +

- - - + + +

Nonnormal - + + + + -

- + + - + -

+ + + - - -

Answers and Solutions: 11 - 217
c. 1. What is the payback period? Find the paybacks for franchises L and S.

Answer: The payback period is the expected number of years required to recover a project's cost. We

calculate the payback by developing the cumulative cash flows as shown below for project l (in

thousands of dollars):

Expected NCF

Year Annual Cumulative

0 ($100) ($100)

1 10 (90)

2 60 Payback is between t = 2

(30)

3 80 50 and t = 3

0 1 2 3

| | | |

-100 10 60
80

-90 -30
+50

Franchise L's $100 investment has not been recovered at the end of year 2, but it has been more

than recovered by the end of year 3. Thus, the recovery period is between 2 and 3 years. If we

assume that the cash flows occur evenly over the year, then the investment is recovered $30/$80 =

$881,718.
The other NPVs were determined in the same manner. If the project is of average risk, it

should be accepted because the expected NPV of the total project is positive.

b. 2NPV = 0.24($881,718 - $117,779)2 + 0.24(-$185,952 - $117,779)2

+ 0.12(-$376,709 - $117,779)2 + 0.4(-$10,000 - $117,779)2

= 198,078,470,853.

NPV = $445,060.

$445,060

CVNPV = = 3.78.

$117,779

Since the CV is 3.78 for this project, while the firm's average project has a CV of 1.0 to

2.0, this project is of high risk.

Answers and Solutions: 11 - 244
SOLUTION TO SPREADSHEET PROBLEM

11-11 The detailed solution for the problem is available both on the instructor's resource CD-ROM (in the

file Solution for FM11 Ch 11 P11 Build a Model.xls) and on the instructor's side of the web site,

http://brigham.swcollege.com.

Answers and Solutions: 11 - 245
MINI CASE

Shrieves Casting Company is considering adding a new line to its product mix, and the capital budgeting
analysis is being conducted by Sidney Johnson, a recently graduated MBA. The production line would
be set up in unused space in Shrieves' main plant. The machinery's invoice price would be
approximately $200,000; another $10,000 in shipping charges would be required; and it would cost an
additional $30,000 to install the equipment. The machinery has an economic life of 4 years, and
Shrieves has obtained a special tax ruling which places the equipment in the MACRS 3-year class. The
machinery is expected to have a salvage value of $25,000 after 4 years of use.

THE NEW LINE WOULD GENERATE INCREMENTAL SALES OF 1,250 UNITS
PER YEAR FOR FOUR YEARS AT AN INCREMENTAL COST OF $100 PER UNIT IN THE
FIRST YEAR, EXCLUDING DEPRECIATION. EACH UNIT CAN BE SOLD FOR $200 IN
THE FIRST YEAR. THE SALES PRICE AND COST ARE EXPECTED TO INCREASE BY
3% PER YEAR DUE TO INFLATION. FURTHER, TO HANDLE THE NEW LINE, THE
FIRM'S NET OPERATING WORKING CAPITAL WOULD HAVE TO INCREASE BY AN
AMOUNT EQUAL TO 12% OF SALES REVENUES. THE FIRM'S TAX RATE IS 40
PERCENT, AND ITS OVERALL WEIGHTED AVERAGE COST OF CAPITAL IS 10
PERCENT.

a. Define "incremental cash flow."

Answer: This is the firm's cash flow with the project minus the firm's cash flow without the project.

a. 1. Should you subtract interest expense or dividends when calculating project cash

flow?

Answer: The cash flow statement should not include interest expense or dividends. The return required

by the investors furnishing the capital is already accounted for when we apply the 10 percent cost

of capital discount rate, hence including financing flows would be "double counting." Put

another way, if we deducted capital costs in the table, and thus reduced the bottom line cash flows,

and then discounted those CFS by the cost of capital, we would, in effect, be subtracting capital

costs twice.

a. 2. Suppose the firm had spent $100,000 last year to rehabilitate the production line site.

Should this cost be included in the analysis? Explain.

Answer: The $100,000 cost to rehabilitate the production line site was incurred last year, and presumably

also expensed for tax purposes. Since, it is a sunk cost, it should not be included in the analysis.

a. 3. Now assume that the plant space could be leased out to another firm at $25,000 a year.

Should this be included in the analysis? If so, how?

Answer: If the plant space could be leased out to another firm, then if Shrieves accepts this project, it

would forgo the opportunity to receive $25,000 in annual cash flows. This represents an

Answers and Solutions: 12 - 246
opportunity cost to the project, and it should be included in the analysis. Note that the

opportunity cost cash flow must be net of taxes, so it would be a $25,000(1 - t) = $25,000(0.6) =

$15,000 annual outflow.

a. 4. Finally, assume that the new product line is expected to decrease sales of the firm's other

lines by $50,000 per year. Should this be considered in the analysis? If so, how?

Answer: If a project affects the cash flows of another project, this is an "externality" which must be

considered in the analysis. If the firm's sales would be reduced by $50,000, then the net cash

flow loss would be a cost to the project. Note that this annual loss would not be the full $50,000,

because Shrieves would save on cash operating costs if its sales dropped. Note also that

externalities can be positive as well as negative.

b. Disregard the assumptions in part a. What is Shrieves' depreciable basis?

Answer: Get the depreciation rates from table 11-2 in the book. Note that because of the half-year

convention, a 3-year project is depreciated over 4 calendar years:

YEAR RATE × BASIS = DEPRECIATION

1 0.33 $240 $ 79

2 0.45 240 108

3 0.15 240 36

4 0.07 240 17

$240

c. Calculate the annual sales revenues and costs (other than depreciation). Why is it

important to include inflation when estimating cash flows?

Answer: With an inflation rate of 3%, the annual revenues and costs are:

Year 1 Year 2 Year 3 Year 4

Units 1250 1250 1250 1250

Unit Price $200.00 $206.00 $212.18 $218.55

Unit Cost $100.00 $103.00 $106.09 $109.27

Sales $250,000 $257,500 $265,225 $273,188

Costs $125,000 $128,750 $132,613 $136,588

The cost of capital is a nominal cost; i.e., it includes a premium for inflation. In other words, it

is larger than the real cost of capital. Similarly, nominal cash flows (those that are inflated) are

larger than real cash flows. If you discount the low, real cash flows with the high, nominal rate,

then the resulting NPV is too low. Therefore, you should always discount nominal cash flows

with a nominal rate, and real cash flows with a real rate. In theory, you could do either way and

get the correct answer. However, there is no accurate way to convert a nominal cost of capital to

a real cost. Therefore, you should inflate cash flows and then discount at the nominal rate.

Answers and Solutions: 12 - 247
c. Calculate the annual sales revenues and costs (other than depreciation). Why is it

important to include inflation when estimating cash flows?

Answer: With an inflation rate of 3%, the annual revenues and costs are:

Here are the annual operating cash flows (in thousands of dollars):

1 2 3 4

Net Revenues $125 $125 $125 $125

Depreciation 79 108 36 17

Before-Tax Income $ 46 $ 17 $ 89 $108

Taxes (40%) 18 7 36 43

Net Income $ 28 $ 10 $ 53 $ 65

Plus Depreciation 79 108 36 17

Net Operating CF $107 $118 $ 89 $ 82

d. Construct annual incremental operating cash flow statements.

Answer:

Year 1 Year 2 Year 3 Year 4

Sales $250,000 $257,500 $265,225 $273,188

Costs $125,000 $128,750 $132,613 $136,588

Depreciation $79,200 $108,000 $36,000 $16,800

Op. EBIT $45,800 $20,750 $96,612 $119,800

Taxes (40%) $18,320 $8,300 $38,645 $47,920

NOPAT $27,480 $12,450 $57,967 $71,880

Depreciation $79,200 $108,000 $36,000 $16,800

Net Operating CF $106,680 $120,450 $93,967 $88,680

e. Estimate the required net operating working capital for each year, and the cash flow due to

investments in net operating working capital.

Answer: The project requires a level of net operating working capital in the amount equal to 12% of the

next year's sales. Any increase in NOWC is a negative cash flow, and any decrease is a positive

cash flow.

Year 0 Year 1 Year 2 Year 3 Year 4

Sales $250,000 $257,500 $265,225 $273,188

NOWC (% of sales) $30,000 $30,900 $31,827 $32,783 $0

CF due to NOWC) ($30,000) ($900) ($927) ($956) $32,783

f. Calculate the after-tax salvage cash flow.

Answers and Solutions: 12 - 248
Answer: When the project is terminated at the end of year 4, the equipment can be sold for $25,000. But,

since it has been depreciated to a $0 book value, taxes must be paid on the full salvage value.

For this project, the after-tax salvage cash flow is:

Salvage Value $25,000

Tax On Salvage Value (10,000)

Net After-Tax Salvage Cash Flow $15,000

g. Calculate the net cash flows for each year? Based on these cash flows, what are the

project's NPV, IRR, MIRR, and payback? Do these indicators suggest that the project

should be undertaken?

Answer: The net cash flows are:

Year 0 Year 1 Year 2 Year 3 Year 4

Initial Outlay ($240,000)

Operating Cash Flows $106,680 $120,450 $93,967 $88,680

CF Due To NOWC ($30,000) ($900) ($927) ($956) $32,783

Salvage Cash Flows $15,000

Net Cash Flows ($270,000) $105,780 $119,523 $93,011 $136,463

NPV = $88,030

IRR = 23.9%

MIRR = 18.0%

Payback = 2.5

h. What does the term "risk" mean in the context of capital budgeting, to what extent can risk

be quantified, and when risk is quantified, is the quantification based primarily on statistical

analysis of historical data or on subjective, judgmental estimates?

Answer: Risk throughout finance relates to uncertainty about future events, and in capital budgeting, this

means the future profitability of a project. For certain types of projects, it is possible to look back

at historical data and to statistically analyze the riskiness of the investment. This is often true

when the investment involves an expansion decision; for example, if Sears were opening a new

store, if Citibank were opening a new branch, or if GM were expanding its Chevrolet plant, then

past experience could be a useful guide to future risk. Similarly, a company that is considering

going into a new business might be able to look at historical data on existing firms in that industry

to get an idea about the riskiness of its proposed investment. However, there are times when it is

impossible to obtain historical data regarding proposed investments; for example, if GM were

considering the development of an electric auto, not much relevant historical data for assessing

the riskiness of the project would be available. Rather, GM would have to rely primarily on the

judgment of its executives, and they, in turn would have to rely on their experience in developing,

manufacturing, and marketing new products. We will try to quantify risk analysis, but you must

Answers and Solutions: 12 - 249
recognize at the outset that some of the data used in the analysis will necessarily be based on

subjective judgments rather than on hard statistical observations.

i. 1. What are the three types of risk that are relevant in capital

budgeting?

2. How is each of these risk types measured, and how do they relate to one another?

Answer: Here are the three types of project risk:

· Stand-alone risk is the project's total risk if it were operated independently.

Stand-alone risk ignores both the firm's diversification among projects and investors'

diversification among firms. Stand-alone risk is measured either by the project's

standard deviation of NPV (NPV) or its coefficient of variation of NPV (CVNPV).

Note that other profitability measures, such as IRR and MIRR, can also be used to

obtain stand-alone risk estimates.

· Within-firm risk is the total riskiness of the project giving consideration to the firm's

other projects, that is, to diversification within the firm. It is the contribution of the

project to the firm's total risk, and it is a function of (a) the project's standard

deviation of NPV and (b) the correlation of the projects' returns with those of the rest

of the firm. Within-firm risk is often called corporate risk, and it is measured by the

project's corporate beta, which is the slope of the regression line formed by plotting

returns on the project versus returns on the firm.

· Market risk is the riskiness of the project to a well-diversified investor, hence it

considers the diversification inherent in stockholders' portfolios. It is measured by

the project's market beta, which is the slope of the regression line formed by plotting

returns on the project versus returns on the market.

i. 3. How is each type of risk used in the capital budgeting process?

Answer: Because management's primary goal is shareholder wealth maximization, the most relevant risk

for capital projects is market risk. However, creditors, customers, suppliers, and employees are

all affected by a firm's total risk. Since these parties influence the firm's profitability, a project's

within-firm risk should not be completely ignored.

Unfortunately, by far the easiest type of risk to measure is a project's stand-alone risk.

Thus, firms often focus on this type of risk when making capital budgeting

decisions. However, this focus does not necessarily lead to poor decisions,

because most projects that a firm undertakes are in its core business. In this

situation, a project's stand-alone risk is likely to be highly correlated with its

within-firm risk, which in turn is likely to be highly correlated with its market

risk.

Answers and Solutions: 12 - 250
j. 1. What is sensitivity analysis?

Answer: Sensitivity analysis measures the effect of changes in a particular variable, say revenues, on a

project's NPV. To perform a sensitivity analysis, all variables are fixed at their expected values

except one. This one variable is then changed, often by specified percentages, and the resulting

effect on NPV is noted. (One could allow more than one variable to change, but this then

merges sensitivity analysis into scenario analysis.)

j. 2. Perform a sensitivity analysis on the unit sales, salvage value, and cost of capital for the

project. Assume that each of these variables can vary from its base case, or expected, value

by plus and minus 10, 20, and 30 percent. Include a sensitivity diagram, and discuss the

results.

Answer: The sensitivity data are given here in tabular form (in thousands of dollars):

NPV Deviation From Base Case

Deviation

From Units

Base Case WACC Sold Salvage

-30% $113,288 $16,668 $84,956

-15% $100,310 $52,348 $86,493

0% $88,030 $88,030 $88,030

15% $76,398 $123,711 $89,567

30% $65,371 $159,392 $91,103

Range 47,916 176,060 6,147

We generated these data with a spreadsheet model in the file ch 11 mini case.xls.

Answers and Solutions: 12 - 251
WACC

Sensitivity Analysis Units Sold

Salvage

$180,000

$160,000

$140,000

$120,000

$100,000
NPV

$80,000

$60,000

$40,000

$20,000

$0

-40% -20% 0% 20% 40%

Deviation from Base-Case Value

A. The sensitivity lines intersect at 0% change and the base case NPV, $81,573. Since all other

variables are set at their base case, or expected values, the zero change situation is the base

case.

B. The plots for unit sales and salvage value are upward sloping, indicating that higher variable

values lead to higher NPVs. Conversely, the plot for cost of capital is downward sloping,

because a higher cost of capital leads to a lower NPV.

C. The plot of unit sales is much steeper than that for salvage value. This indicates that NPV is

more sensitive to changes in unit sales than to changes in salvage value.

D. Steeper sensitivity lines indicate greater risk. Thus, in comparing two projects, the one with

the steeper lines is considered to be riskier.

Answers and Solutions: 12 - 252
j. 3. What is the primary weakness of sensitivity analysis? What is its primary usefulness?

Answer: The two primary disadvantages of sensitivity analysis are (1) that it does not reflect the effects of

diversification and (2) that it does not incorporate any information about the possible magnitudes

of the forecast errors. Thus, a sensitivity analysis might indicate that a project's NPV is highly

sensitive to the sales forecast, hence that the project is quite risky, but if the project's sales, hence

its revenues, are fixed by a long-term contract, then sales variations may actually contribute little

to the project's risk. It also ignores any relationships between variables, such as unit sales and

sales price.
Therefore, in many situations, sensitivity analysis is not a particularly good indicator of

risk. However, sensitivity analysis does identify those variables which

potentially have the greatest impact on profitability, and this helps management

focus its attention on those variables that are probably most important.

k. Assume that Sidney Johnson is confident of her estimates of all the variables that affect the

@ Year 2 of Low CF Scenario is $6.974 and PV @ Year 2 of High CF Scenario is $13.313. So the

PV is:

P = [0.1(6.974)+ 0.9(13.313] / 1.102 = $10.479.

X = $9.

t = 2.

rRF = 0.06.

2 = 0.0111.

d1 = ln[10.479/9] + [0.06 + .5(.0111)](2) = 1.9010

(.0111)0.5 (2)0.5

d2 = 1.9010 - (.0111)0.5 (2)0.5 = 1.7520

From Excel function NORMSDIST, or approximated from Table 12E-1 in Extension to Chapter 12:

N(d1) = 0.9713

N(d2) = 0.9601

Using the Black-Scholes Option Pricing Model, you calculate the option's value as:

-r t

V = P[N(d1)] - Xe RF [N(d2)]

= $10.479(0.9713) - $9e(-0.06)(2)(0.9601)

= $10.178 - $7.664

= $2.514 million.

Answers and Solutions: 12 - 262
SOLUTION TO SPREADSHEET PROBLEMS

12-7 The detailed solution for the problem is available both on the instructor's resource CD-ROM (in the

file Solution for FM11 Ch 12 P7 Build a Model.xls) and on the instructor's side of the textbook's web

site, http://brigham.swcollege.com.

Answers and Solutions: 12 - 263
MINI CASE

Assume that you have just been hired as a financial analyst by Tropical Sweets Inc., a mid-sized
California company that specializes in creating exotic candies from tropical fruits such as
mangoes, papayas, and dates. The firm's CEO, George Yamaguchi, recently returned from an
industry corporate executive conference in San Francisco, and one of the sessions he attended
was on real options. Since no one at Tropical Sweets is familiar with the basics of real options,
Yamaguchi has asked you to prepare a brief report that the firm's executives could use to gain at
least a cursory understanding of the topics.

To begin, you gathered some outside materials the subject and used these materials to draft a list of
pertinent questions that need to be answered. In fact, one possible approach to the paper is to use a
question-and-answer format. Now that the questions have been drafted, you have to develop the answers.

a. What are some types of real options?

Answer: 1. Investment timing options

2. Growth options

a. Expansion of existing product line

b. New products

c. New geographic markets

3. Abandonment options

a. Contraction

b. Temporary suspension

c. Complete abandonment

4. Flexibility options.

b. What are five possible procedures for analyzing a real option?

Answer: 1. DCF analysis of expected cash flows, ignoring option.

2. Qualitatively assess the value of the real option.

3. Decision tree analysis.

4. Use a model for a corresponding financial option, if possible.

5. Use financial engineering techniques if a corresponding financial option is not available.

Answers and Solutions: 13 - 264
c. Tropical Sweets is considering a project that will cost $70 million and will generate

expected cash flows of $30 per year for three years. The cost of capital for this type

of project is 10 percent and the risk-free rate is 6 percent. After discussions with the

marketing department, you learn that there is a 30 percent chance of high demand,

with future cash flows of $45 million per year. There is a 40 percent chance of

average demand, with cash flows of $30 million per year. If demand is low (a 30

percent chance), cash flows will be only $15 million per year. What is the expected

NPV?

Answer: Initial Cost = $70 Million

Expected Cash Flows = $30 Million Per Year For Three Years

Cost Of Capital = 10%

PV Of Expected CFs = $74.61 Million

Expected NPV = $74.61 - $70

= $4.61 Million

Alternatively, one could calculate the NPV of each scenario:

Demand Probability Annual Cash Flow

High 30% $45

Average 40% $30

Low 30% $15

Find NPV of each scenario:

PV High: N=3 I=10 PV=? PMT=-45 FV=0

PV= 111.91

NPV High = $111.91 - $70 = $41.91 Million.

PV Average: N=3 I=10 PV=? PMT=-30 FV=0

PV= 74.61

NPV Average = $74.61 - $70 = $4.71 Million.

PV Low: N=3 I=10 PV=? PMT=-15 FV=0

PV= 37.30

NPV Low = $37.30 - $70 = -$32.70 Million.

Find Expected NPV:

E(NPV)=.3($41.91)+.4($4.61)+.3(-$32.70)

E(PV)= $4.61.

d. Now suppose this project has an investment timing option, since it can be delayed for

a year. The cost will still be $70 million at the end of the year, and the cash flows

for the scenarios will still last three years. However, Tropical Sweets will know the

level of demand, and will implement the project only if it adds value to the company.

The direct approach gives an estimate of 18.2% for the variance of the project's return.

Answers and Solutions: 13 - 268
The indirect approach:
Given a current stock price and an anticipated range of possible stock prices at some point in the
future, we can use our knowledge of the distribution of stock returns (which is lognormal) to
relate the variance of the stock's rate of return to the range of possible outcomes for stock price.
To use this formula, we need the coefficient of variation of stock price at the time the option
expires. To calculate the coefficient of variation, we need the expected stock price and the
standard deviation of the stock price (both of these are measured at the time the option expires).
For the real option, we need the expected value of the project's cash flows at the date the real
option expires, and the standard deviation of the project's value at the date the real option expires.
We previously calculated the value of the project at the time the option expires, and we can use
this to calculate the expected value and the standard deviation.

Here is a formula for the variance of a stock's return, if you know the coefficient of variation of
the expected stock price at some point in the future. The CV should be for the entire project,
including all scenarios:
2 = LN[CV2 + 1]/T = LN[0.392 + 1]/1 = 14.2%.

This is lower than the variance found for the previous option because the dispersion of cash flows
for the replication project is the same as for the original, even though the replication occurs much
later. Therefore, the rate of return for the replication is less volatile. We do sensitivity analysis
later.

The indirect approach:
First, find the coefficient of variation for the value of the project at the time the option expires
(year 3).

We previously calculated the value of the project at the time the option expires, and we can use
this to calculate the expected value and the standard deviation.

b. Common equity is determined at a point in time, say December 31, 2004. Profits are earned over

time, say during 2004. If a firm is growing rapidly, year-end equity will be much larger than

beginning-of-year equity, so the calculated rate of return on equity will be different depending on

whether end-of-year, beginning-of-year, or average common equity is used as the denominator.

Average common equity is conceptually the best figure to use. In public utility rate cases, people

are reported to have deliberately used end-of-year or beginning-of-year equity to make returns on

equity appear excessive or inadequate. Similar problems can arise when a firm is being

evaluated.

13-6 Firms within the same industry may employ different accounting techniques, which make it difficult

to compare financial ratios. More fundamentally, comparisons may be misleading if firms in the

Answers and Solutions: 13 - 275
same industry differ in their other investments. For example, comparing Pepsico and Coca-Cola may
be misleading because apart from their soft drink business, Pepsi also owns other businesses such as
Frito-Lay, Pizza Hut, Taco Bell, and KFC.

Answers and Solutions: 13 - 276
SOLUTIONS TO END-OF-CHAPTER PROBLEMS

CA CA - I
13-1 CA = $3,000,000; = 1.5; = 1.0;

CL CL

CL = ?; I = ?

CA

= 1.5

CL

$3,000,000

= 1.5

CL

1.5 CL = $3,000,000

CL = $2,000,000.

CA - I

= 1.0

CL

$3,000,000 - I

= 1.0

$2,000,000

$3,000,000 - I = $2,000,000

I = $1,000,000.

13-2 DSO = 40 days; ADS = $20,000; AR = ?

AR

DSO =

S

365

AR

40 =

$20,000

AR = $800,000.

13-3 A/E = 2.4; D/A = ?

Answers and Solutions: 13 - 277

D 1

= 1 -

A A

E

D 1

= 1 -

A 2.4

D

= 0.5833 = 58.33%.

A
13-4 ROA = 10%; PM = 2%; ROE = 15%; S/TA = ?; A/E = ?

ROA = NI/A; PM = NI/S; ROE = NI/E

ROA = PM × S/TA

NI/A = NI/S × S/TA

10% = 2% × S/TA

S/TA = 5.

ROE = PM × S/TA × TA/E

NI/E = NI/S × S/TA × TA/E

15% = 2% × 5 × TA/E

15% = 10% × TA/E

TA/E = 1.5.

13-5 We are given ROA = 3% and Sales/Total assets = 1.5×.

From Du Pont equation: ROA = Profit margin × Total assets turnover

3% = Profit margin (1.5)

Answers and Solutions: 13 - 278
Profit margin = 3%/1.5 = 2%.

We can also calculate the company's debt ratio in a similar manner, given the facts of the problem.

We are given ROA(NI/A) and ROE(NI/E); if we use the reciprocal of ROE we have the following

equation:

E NI E D E

= _ and =1- , so

A A NI A A

E 1

= 3% _

A 0.05

E

= 60% .

A

D

= 1 - 0.60 = 0.40 = 40% .

A

Alternatively,

ROE = ROA × EM

5% = 3% × EM

EM = 5%/3% = 5/3 = TA/E.

Take reciprocal:

E/TA = 3/5 = 60%;

therefore,

D/A = 1 - 0.60 = 0.40 = 40%.

Thus, the firm's profit margin = 2% and its debt ratio = 40%.

$1,312,500
13-6 Present current ratio = = 2.5.

$525,000

$1,312,500 + NP

Minimum current ratio = = 2.0.

$525,000 + NP

$1,312,500 + NP = $1,050,000 + 2NP

NP = $262,500.

Answers and Solutions: 13 - 279
Short-term debt can increase by a maximum of $262,500 without violating a 2 to 1 current ratio,

assuming that the entire increase in notes payable is used to increase current assets. Since we

assumed that the additional funds would be used to increase inventory, the inventory account will

c. The firm's days sales outstanding is more than twice as long as the industry average, indicating

that the firm should tighten credit or enforce a more stringent collection policy. The total assets

turnover ratio is well below the industry average so sales should be increased, assets decreased, or

both. While the company's profit margin is higher than the industry average, its other

profitability ratios are low compared to the industry--net income should be higher given the

amount of equity and assets. However, the company seems to be in an average liquidity position

and financial leverage is similar to others in the industry.

d. If 2004 represents a period of supernormal growth for the firm, ratios based on this year will be

distorted and a comparison between them and industry averages will have little meaning.

Potential investors who look only at 2003 ratios will be misled, and a return to normal conditions

in 2005 could hurt the firm's stock price.

13-10 1. Debt = (0.50)(Total assets) = (0.50)($300,000) = $150,000.

2. Accounts payable = Debt ­ Long-term debt = $150,000 - $60,000

= $90,000

Total liabilities

3. Common stock = - Debt - Retained earnings

and equity

= $300,000 - $150,000 - $97,500 = $52,500.

4. Sales = (1.5)(Total assets) = (1.5)($300,000) = $450,000.

5. Inventory = Sales/5 = $450,000/5 = $90,000.

6. Accounts receivable = (Sales/365)(DSO) = ($450,000/365)(36.5)

= $45,000.

7. Cash + Accounts receivable = (0.80)(Accounts payable)

Cash + $45,000 = (0.80)($90,000)

Cash = $72,000 - $45,000 = $27,000.

8. Fixed assets = Total assets - (Cash + Accts rec. + Inventories)

= $300,000 - ($27,000 + $45,000 + $90,000) = $138,000.

9. Cost of goods sold = (Sales)(1 - 0.25) = ($450,000)(0.75)

= $337,500.

Answers and Solutions: 13 - 282
13-11 a. Here are the firm's base case ratios and other data as compared to the industry:

Firm
Industry Comment

Quick 0.8× 1.0×

Weak

Current 2.3 2.7

Weak

Inventory turnover 4.8 7.0 Poor

Days sales outstanding 37 days 32 days
Poor

Fixed assets turnover 10.0× 13.0×
Poor

Total assets turnover 2.3 2.6
Poor

Return on assets 5.9% 9.1%
Bad

Return on equity 13.1 18.2
Bad

Debt ratio 54.8 50.0
High

Profit margin on sales 2.5 3.5
Bad

EPS $4.71
n.a. --

Stock Price $23.57 n.a.
--

P/E ratio 5.0×
6.0× Poor

P/CF ratio 2.0×
3.5× Poor

M/B ratio 0.65 n.a.
--

The firm appears to be badly managed--all of its ratios are worse than the industry averages, and

the result is low earnings, a low P/E, P/CF ratio, a low stock price, and a low M/B ratio. The

company needs to do something to improve.

b. A decrease in the inventory level would improve the inventory turnover, total assets turnover, and

ROA, all of which are too low. It would have some impact on the current ratio, but it is difficult

to say precisely how that ratio would be affected. If the lower inventory level allowed the

company to reduce its current liabilities, then the current ratio would improve. The lower cost of

goods sold would improve all of the profitability ratios and, if dividends were not increased,

would lower the debt ratio through increased retained earnings. All of this should lead to a

higher market/book ratio and a higher stock price.

Answers and Solutions: 13 - 283
SOLUTION TO SPREADSHEET PROBLEM

13-12 The detailed solution for the

problem is available both on the instructor's resource CD-ROM (in the file Solution to FM11 Ch 13

P12 Build a Model.xls) and on the instructor's side of the web site, http://brigham.swcollege.com.

Answers and Solutions: 13 - 284
MINI CASE

The first part of the case, presented in chapter 3, discussed the situation that Computron
Industries was in after an expansion program. Thus far, sales have not been up to the
forecasted level, costs have been higher than were projected, and a large loss occurred in
2004, rather than the expected profit. As a result, its managers, directors, and investors
are concerned about the firm's survival.

Donna Jamison was brought in as assistant to Fred Campo, Computron's chairman,
who had the task of getting the company back into a sound financial position. Computron's
2003 and 2004 balance sheets and income statements, together with projections for 2005,
are shown in the following tables. Also, the tables show the 2003 and 2004 financial ratios,
along with industry average data. The 2005 projected financial statement data represent
Jamison's and Campo's best guess for 2005 results, assuming that some new financing is
arranged to get the company "over the hump."

Jamison examined monthly data for 2004 (not given in the case), and she detected an
improving pattern during the year. Monthly sales were rising, costs were falling, and
large losses in the early months had turned to a small profit by December. Thus, the
annual data looked somewhat worse than final monthly data. Also, it appears to be taking
longer for the advertising program to get the message across, for the new sales offices to
generate sales, and for the new manufacturing facilities to operate efficiently. In other
words, the lags between spending money and deriving benefits were longer than
Computron's managers had anticipated. For these reasons, Jamison and Campo see hope
for the company--provided it can survive in the short run.

Jamison must prepare an analysis of where the company is now, what it must do to
regain its financial health, and what actions should be taken. Your assignment is to help
her answer the following questions. Provide clear explanations, not yes or no answers.

Target FA = 0.25($2,000) = $500 = Required FA. Since the firm currently has $500 of

fixed assets, no new fixed assets will be required.

Addition to RE = M(S1)(1 - Payout ratio) = 0.05($2,000)(0.4) = $40.

Answers and Solutions: 14 - 304
SOLUTION TO SPREADSHEET PROBLEM

14-10 The detailed solution for the spreadsheet problem is available both on the instructor's resource

CD-ROM (in the file Solution to FM11 Ch 14 -10 Build a Model.xls) and on the instructor's side of

the web site, http://brigham.swcollege.com.

Answers and Solutions: 14 - 305
MINI CASE

Betty Simmons, the new financial manager of Southeast Chemicals (SEC), a Georgia
producer of specialized chemicals for use in fruit orchards, must prepare a financial
forecast for 2005. SEC's 2004 sales were $2 billion, and the marketing department is
forecasting a 25 percent increase for 2005. Simmons thinks the company was operating at
full capacity in 2004, but she is not sure about this. The 2004 financial statements, plus
some other data, are shown below.

Assume that you were recently hired as Simmons' assistant, and your first major
task is to help her develop the forecast. She asked you to begin by answering the
following set of questions.

Financial Statements And Other Data On SEC

(Millions Of Dollars)
A. 2004 Balance Sheet % of
% of

sales
sales

Cash & Securities $ 20 1% Accounts Payable

And Accruals $ 100 5%

Accounts Receivable 240 12 Notes Payable 100

Inventory 240 12 Total Current Liabilities $ 200

Total Current Assets $ 500 Long-Term Debt 100

Net Fixed Assets 500 25 Common Stock 500

Retained Earnings 200

Total Assets $1,000 Total Liabilities And Equity $1,000

B. 2004 Income Statement % of

sales

Sales $2,000.00

Cost Of Goods Sold (COGS) 1,200.00 60%

Sales, General, And Administrative Costs 700.00 35

Earnings Before Interest And Taxes $ 100.00

Interest 10.00

Earnings Before Taxes $ 90.00

Taxes (40%) 36.00

Net Income $ 54.00

Dividends (40%) $ 21.60

Addition To Retained Earnings $ 32.40

Answers and Solutions: 15 - 306
C. Key Ratios Sec
Industry

Profit Margin 2.70 4.00

Return On Equity 7.71 15.60

Days Sales Outstanding (365 Days) 43.80 Days 32.00 Days

Inventory Turnover 8.33× 11.00×

Fixed Assets Turnover 4.00 5.00

Debt/Assets 30.00% 36.00%

Times Interest Earned 10.00× 9.40×

Current Ratio 2.50 3.00

Return On Invested Capital

(NOPAT/Operating Capital) 6.67% 14.00%

a. Describe three ways that pro forma statements are used in financial planning.

Answer: Three important uses: (1) forecast the amount of external financing that will be required, (2)

evaluate the impact that changes in the operating plan have on the value of the firm, (3) set

The firm's optimal capital structure is that capital structure which minimizes the firm's

WACC. Elliott's WACC is minimized at a capital structure consisting of 40% debt and

60% equity. At that capital structure, the firm's WACC is 11.45%.

. Answers and Solutions: 16 - 333
SOLUTION TO SPREADSHEET PROBLEM

16-7 The detailed solution for the problem is available both on the instructor's resource CD-ROM (in the

file Solution for FM11 Ch 16 P7 Build a Model.xls) and on the instructor's side of the web site,

http://brigham.swcollege.com.

. Answers and Solutions: 16 - 334
MINI CASE

Assume you have just been hired as business manager of PizzaPalace, a pizza restaurant
located adjacent to campus. The company's EBIT was $500,000 last year, and since the
university's enrollment is capped, EBIT is expected to remain constant (in real terms) over
time. Since no expansion capital will be required, PizzaPalace plans to pay out all
earnings as dividends. The management group owns about 50 percent of the stock, and
the stock is traded in the over-the-counter market.

The firm is currently financed with all equity; it has 100,000 shares outstanding; and
P0 = $25 per share. When you took your MBA Corporate Finance course, your instructor stated that
most firms' owners would be financially better off if the firms used some debt. When you suggested
this to your new boss, he encouraged you to pursue the idea. As a first step, assume that you obtained
from the firm's investment banker the following estimated costs of debt for the firm at different capital
structures:

% Financed With Debt Rd

0% ---

20 8.0%

30 8.5

40 10.0

50 12.0

If the company were to recapitalize, debt would be issued, and the funds received would be
used to repurchase stock. PizzaPalace is in the 40 percent state-plus-federal corporate tax
bracket, its beta is 1.0, the risk-free rate is 6 percent, and the market risk premium is 6
percent.

a. Provide a brief overview of capital structure effects. Be sure to identify the ways in which

capital structure can affect the weighted average cost of capital and free cash flows.

Answer: The basic definitions are:

(1) V = Value Of Firm

(2) FCF = Free Cash Flow

(3) WACC = Weighted Average Cost Of Capital

(4) Rs And Rd are costs of stock and debt

(5) We And Wd are percentages of the firm that are financed with stock and debt.

The impact of capital structure on value depends upon the effect of debt on: WACC and/or FCF.

This gives an option value of $3.32 million. The debt value is then 5.0 ­ 3.23 =

$1.77 million. Its yield is 6.8%. The value of the stock goes down and the

value of the debt goes up because with lower risk, Fethe has less of a chance of a

"home run."

Answers and Solutions: 17 - 354
SOLUTION TO SPREADSHEET PROBLEM

17-8 The detailed solution for the problem is available both on the instructor's resource CD-ROM (in the

file Solution for FM11 Ch 17 P8 Build a Model.xls) and on the instructor's side of the web site,

http://brigham.swcollege.com.

Solution to Spreadsheet Problem: 15 - 355
MINI CASE

David Lyons, CEO of Lyons Solar Technologies, is concerned about his firm's level of debt
financing. The company uses short-term debt to finance its temporary working capital
needs, but it does not use any permanent (long-term) debt. Other solar technology
companies average about 30 percent debt, and Mr. Lyons wonders why they use so much
more debt, and what its effects are on stock prices. To gain some insights into the matter,
he poses the following questions to you, his recently hired assistant:

a. Business Week recently ran an article on companies' debt policies, and the names Modigliani

and Miller (MM) were mentioned several times as leading researchers on the theory of

capital structure. Briefly, who are MM, and what assumptions are embedded in the MM

and Miller models?

Answer: Modigliani and Miller (MM) published their first paper on capital structure (which assumed zero

taxes) in 1958, and they added corporate taxes in their 1963 paper. Modigliani won the Nobel

Prize in economics in part because of this work, and most subsequent work on capital structure

theory stems from MM. Here are their assumptions:

· Firms' business risk can be measured by EBIT, and firms with the same degree of

risk can be grouped into homogeneous business risk classes.

· All investors have identical (homogeneous) expectations about all firms' future

earnings.

· There are no transactions (brokerage) costs, either to individuals or to firms.

· All debt is riskless, and both individuals and corporations can borrow unlimited

amounts of money at the same risk-free rate.

· All cash flows are perpetuities. This implies that firms and individuals issue

perpetual debt, and also that firms pay out all earnings as dividends, hence have

zero growth. Additionally, this implies that expected EBIT is constant over time,

although realized EBIT may turn out to be higher or lower than was expected.

· In their first paper (1958), MM also assumed that there are no corporate or

personal taxes.

Mini Case: 17 - 356
These assumptions--all of them--were necessary in order for MM to use the arbitrage

argument to develop and prove their equations. If the assumptions are unrealistic,

then the results of the model are not guaranteed to hold in the real world.

b. Assume that firms U and L are in the same risk class, and that both have EBIT = $500,000.

Firm U uses no debt financing, and its cost of equity is rsU = 14%. Firm L has $1 million of

debt outstanding at a cost of rd = 8%. There are no taxes. Assume that the MM

assumptions hold, and then:

1. Find v, s, rs, and WACC for firms U and L.

Answer: First, we find Vu and VL:

EBIT $500,000

VU = = = $3,571,429.

rsU 0.14

VL = VU = $3,571,429.

To find rsL, it is necessary first to find the market values of firm L's debt and equity. The value

of its debt is stated to be $1,000,000. Therefore, we can find s as follows:

D + SL = VL

SL = VL - D = $3,571,429 - $1,000,000 = $2,571,429.

Mini Case: 17 - 357
Now we can find L's cost of equity, rsL:

rsL = rsU + (rsU - rd)(D/S)

= 14.0% + (14.0% - 8.0%)($1,000,000/$2,571,429)

= 14.0% + 2.33% = 16.33%.

We know from Proposition I that the WACC must be WACC = rsU = 14.0% for all firms in this

risk class, regardless of leverage, but this can be verified using the WACC formula:

WACC = wdrd + wcers = (D/V)rd + (S/V)rs

= ($1,000/$3,571)(8.0%) + ($2,571/$3,571)(16.33%)

= 2.24% + 11.76% = 14.0%.

b. 2. Graph (a) the relationships between capital costs and leverage as measured by D/V,

This represents a 40% decline in value, and it is logical, because the 40% tax rate takes

away 40% of the income and hence 40% of the firm's value.

Looking at VL, we see that:

VL = VU + TD = $2,142,857 + 0.4($1,000,000)

VL = $2,142,857 + $400,000 - $2,542,857 versus $2,142,857 for VU.

Thus, the use of $1,000,000 of debt financing increases firm value by T(D) = $400,000

over its leverage-free value.

To find rsL, it is first necessary to find the market value of the equity:

D + SL = VL

$1,000,000 + SL = $2,542,857

SL = $1,542,857.

now,

rsL = rsU + (rsU - rd)(1 - T)(D/S)

= 14.0% + (14.0% - 8.0%)(0.6)($1,000/$1,543)

= 14.0% + 2.33% = 16.33%.

Mini Case: 17 - 360
Firm L's WACC is 11.8 percent:

WACCL = (D/V)rd(1 - T) + (S/V)rs

= ($1,000/$2,543)(8%)(0.6) + (1,543/$2,543)(16.33%)

= 1.89% + 9.91% = 11.8%.

The WACC is lower for the leveraged firm than for the unleveraged firm when corporate taxes are
considered.

Figure 3 below plots capital costs at different D/V ratios under the MM model with corporate
taxes. Here the WACC declines continuously as the firm uses more and more debt, whereas the
WACC was constant in the without-tax model. This result occurs because of the tax
deductibility of debt financing (interest payments), which impacts the graph in two ways: (1) the
cost of debt is lowered by (1 - T), and (2) the cost of equity increases at a slower rate when
corporate taxes are considered because of the (1 - T) term in Proposition II. The combined effect
produces the downward-sloping WACC curve.

Figure 4 shows that, when corporate taxes are considered, the firm's value increases
continuously as more and more debt is used.

Figure 3

rs

With Taxes

WACC

50%

rd x (1-T)

45%

40%

Cost of Capital

35%

30%

25%

20%

15%

10%

5%

0%

0% 20% 40% 60% 80% 100%

Debt/Value Ratio

Mini Case: 17 - 361
Figure 4

Value of Firm, V

($)

4

VL

3

TD

2 VU

1

0 0.5 1.0 1.5 2.0 2.5

Debt ($)

(Millions of $)

d. Now suppose investors are subject to the following tax rates:

TD = 30% and TS = 12%.

1. What is the gain from leverage according to the miller model?

Answer: To begin, note that Miller's Proposition I is stated as follows:

(1 - TC )(1 - TS )

VL = VU + 1 - D.

(1 - TD )

Here the bracketed term replaces T in the earlier MM tax model, and

Tc = corporate tax rate, Td = personal tax rate on debt income, and

Ts = personal tax rate on stock income.

If there are no personal or corporate taxes, then Tc = Ts = Td = 0, and Miller's model

simplifies to

VL = VU,

Which is the same as in MM's 1958 model, which assumed zero taxes.

If there are corporate taxes, but no personal taxes, then Ts = Td = 0, and Miller's model

simplifies to

VL = VU + TCD,

Which is the same as MM obtained in their 1963 article, which considered only corporate taxes.

that L's volatility is 0.60 ( = 0.60) and that the risk free rate is 6 percent.

Answer: L's equity can be considered as a call option on the total value of l with an exercise price of $2

million, and an expiration date in one year. If the value of L's operations is less than $2 million

in a year, then L's management will not be able to make its required payment on the debt, and the

firm will be bankrupt. The debtholders will take over the firm and the equity holders will

receive nothing. If L's value is greater than $2 million in one year, then management will repay

the debt and the stockholders will keep the company.

This option can be valued with the Black-Scholes Option Pricing Model:

V = PN(D1) ­ Xe-RTN(D2)

where

D1 = [ln(P/X) + (r + 0.52)T]/[T0.5]

D2 = D1 - T0.5

And n() is the cumulative normal distribution function, from either appendix a in the back of the

text, or the NORMSDIST() function in excel.

in this case, P = $4

X = $2

= 0.60

T = 1.0

R = 0.06

and calculating,

D1 = 1.552

D2 = 0.9552

N(D1) = 0.9491

N(D2) = 0.8303

Answers and Solutions: 18 - 366
and V = $2.1964 million.

This leaves debt value of $4 million - $2.1964 million = $1.8036 million.

The yield on this debt is calculated as

Price = (Face Value)/(1+Yield)N

so that

Yield = [Face Value/Price]1/N ­ 1.0

= [2.0/1.8036] ­ 1.0

= 10.89%

In this case, the value of the debt must be $1.8036 million, and it is yielding 10.89%. The value

of the equity is $2.1964 million.

h. What is the value of L's stock for volatilites between 0.20 and 0.95? What

in-centives might the manager of L have if she understands this relationship? What

might debtholders do in response?

Answer: The mini case model shows the calculations for the table below.

Value of Stock and Debt for

Different Volatilities

Volatility Equity Debt

0.20 2.12 1.88

0.25 2.12 1.88

0.30 2.12 1.88

0.35 2.12 1.88

0.40 2.13 1.87

0.45 2.14 1.86

0.50 2.16 1.84

0.55 2.17 1.83

0.60 2.20 1.80

0.65 2.22 1.78

0.70 2.25 1.75

0.75 2.28 1.72

0.80 2.31 1.69

0.85 2.34 1.66

0.90 2.38 1.62

0.95 2.41 1.59

Answers and Solutions: 18 - 367
The value of the equity increases as the volatility increases--and the value of the debt decreases
as well. A manager who knows this may choose to invest the proceeds from borrowing in assets
that are riskier than usual. This is called "bait and switch." This action decreases the value of
the debt, because now its claim is riskier. It increases the value of equity because the worse the
stockholders can do is default on the bonds, but the best they can do is potentially unlimited.

Bondholders who face this possibility will write covenants into their bond contracts limiting
management's ability to invest in assets other than originally planned. If this isn't possible, then
bondholders will demand a higher rate of return in order to compensate them for the possibility
that management will switch investments.

Answers and Solutions: 18 - 368
Chapter 18

Distributions to Shareholders:

Dividends and Repurchases

ANSWERS TO END-OF-CHAPTER QUESTIONS

18-1 a. The optimal distribution policy is one that strikes a balance between dividend yield and capital

gains so that the firm's stock price is maximized.

b. The dividend irrelevance theory holds that dividend policy has no effect on either the price of a

firm's stock or its cost of capital. The principal proponents of this view are Merton Miller and

Franco Modigliani (MM). They prove their position in a theoretical sense, but only under strict

assumptions, some of which are clearly not true in the real world. The "bird-in-the-hand" theory

assumes that investors value a dollar of dividends more highly than a dollar of expected capital

gains because the dividend yield component, D1/P0, is less risky than the g component in the total

18-10 The detailed solution for the problem is available both on the instructor's resource CD-ROM (in the

file Solution for FM11 Ch 18 P10 Build a Model.xls) and on the instructor's side of the web site,

http://brigham.swcollege.com.

Answers and Solutions: 18 - 377
MINI CASE

Southeastern Steel Company (SSC) was formed 5 years ago to exploit a new
continuous-casting process. SSC's founders, Donald Brown and Margo Valencia, had
been employed in the research department of a major integrated-steel company, but when
that company decided against using the new process (which Brown and Valencia had
developed), they decided to strike out on their own. One advantage of the new process
was that it required relatively little capital in comparison with the typical steel company, so
Brown and Valencia have been able to avoid issuing new stock, and thus they own all of the
shares. However, SSC has now reached the stage where outside equity capital is
necessary if the firm is to achieve its growth targets yet still maintain its target capital
structure of 60 percent equity and 40 percent debt. Therefore, Brown and Valencia have
decided to take the company public. Until now, Brown and Valencia have paid
themselves reasonable salaries but routinely reinvested all after-tax earnings in the firm, so
dividend policy has not been an issue. However, before talking with potential outside
investors, they must decide on a dividend policy.

Assume that you were recently hired by Arthur Adamson & Company (AA), a
national consulting firm, which has been asked to help SSC prepare for its public offering.
Martha Millon, the senior AA consultant in your group, has asked you to make a
presentation to Brown and Valencia in which you review the theory of dividend policy and
discuss the following questions.

a. 1. What is meant by the term "distribution policy"?

Answer: Distribution policy is defined as the firm's policy with regard to (1) the level of distributions, (2)

the form of distributions (dividends or stock repurchases), and (3) the stability of distributions.

a. 2. The terms "irrelevance," "bird-in-the-hand," and "tax preference" have been

used to describe three major theories regarding the way dividend payouts affect a

firm's value. Explain what these terms mean, and briefly describe each theory.

Answer: Dividend irrelevance refers to the theory that investors are indifferent between dividends and

Answers and Solutions: 19 - 378
capital gains, making dividend policy irrelevant with regard to its effect on the value of the firm.

"Bird-in-the-hand" refers to the theory that a dollar of dividends in the hand is preferred by

investors to a dollar retained in the business, in which case dividend policy would affect a firm's

value.

The dividend irrelevance theory was proposed by MM, but they had to make some very

Using a financial calculator, enter the cash flows into the cash flow register, I = 6, NPV = ?

NPV = $2,717,128.

b. The company should consider what interest rates might be next year. If there is a high

probability that rates will drop below the current rate, it may be more advantageous to refund

later versus now. If there is a high probability that rates will increase, the firm should act

now to refund the old issue. Also, the company should consider how much ill will is created

with investors if the issue is called. If Tarpon is highly dependent on a small group of

investors, it would want to avoid future difficulty in obtaining financing. However, bond

issues are callable after a certain time and investors expect them to be called if rates drop

considerably.

Answers and Solutions: 19 - 396
SOLUTION TO SPREADSHEET PROBLEM

19-6 The detailed solution for the problem is available both on the instructor's resource CD-ROM (in the

file Solution for FM11 Ch 19 P6 Build a Model.xls) and on the instructor's side of the web site,

http://brigham.swcollege.com.

Answers and Solutions: 19 - 397
MINI CASE

Randy's, a family-owned restaurant chain operating in Alabama, has grown to the point
where expansion throughout the entire southeast is feasible. The proposed expansion
would require the firm to raise about $15 million in new capital. Because Randy's
currently has a debt ratio of 50 percent, and also because the family members already have
all their personal wealth invested in the company, the family would like to sell common
stock to the public to raise the $15 million. However, the family does want to retain voting
control. You have been asked to brief the family members on the issues involved by
answering the following questions:

a. What agencies regulate securities markets?

Answer: The main agency that regulates the securities market is the Securities And Exchange Commission.

Some of the responsibilities of the SEC include: regulation of all national stock

exchanges--companies whose securities are listed on an exchange must file annual reports with

the SEC; prohibiting manipulation by pools or wash sales; controls over trading by corporate

insiders; and control over the proxy statement and how it is used to solicit votes.

The Federal Reserve Board controls flow of credit into security transactions through

margin requirements. States also have some control over the issuance of new

securities within their boundaries. The securities industry itself realizes the

importance of stable markets, therefore, the various exchanges work closely with the

sec to police transactions and to maintain the integrity and credibility of the system.

Mini Case: 19 - 398
b. How are start-up firms usually financed?

Answer: The first financing comes from the founders. The first external financing comes from angels,

who are wealthy individuals. The next external financing comes from a venture capital fund.

The fund raises capital from institutional investors, usually around $70 to $80 million. The

managers of the fund are called venture capitalists. The fund invests in ten to twelve companies,

and the venture capitalist sits on their boards.

c. Differentiate between a private placement and a public offering.

Answer: In a private placement stock is sold directly to one or a small group of investors rather than being

distributed to the public at large. A private placement has the advantage of lower flotation costs;

however, since the stock would be bought by a small number of outsiders, it would not be actively

traded, and a liquid market would not exist. Further, since it would not have gone through the

SEC registration process, the holders would be unable to sell it except to a restricted set of

"sophisticated" investors. Further, it might be difficult to find investors willing to invest large

sums in the company and yet be minority stockholders. Thus, many of the advantages listed

above would not be obtained. For these reasons, a public placement makes more sense in

Randy's situation.

d. Why would a company consider going public? What are some advantages and

disadvantages?

Answer: A firm is said to be "going public" when it sells stock to the public for the first time. A

company's first stock offering to the public is called an "initial public offering (IPO)." Thus,

Randy's will go public if it goes through with its planned IPO. There are several advantages and

disadvantages to going public:

Mini Case: 19 - 399
Advantages to going public:

· Going public will allow the family members to diversify their assets and reduce the

riskiness of their personal portfolios.

· It will increase the liquidity of the firm's stock, allowing the family stockholders to

sell some stock if they need to raise cash.

· It will make it easier for the firm to raise funds. The firm would have a difficult

time trying to sell stock privately to an investor who was not a family member.

Outside investors would be more willing to purchase the stock of a publicly held

corporation which must file financial reports with the sec.

· Going public will establish a value for the firm.

Disadvantages to going public:

· The firm will have to file financial reports with the SEC and perhaps with state

officials. There is a cost involved in preparing these reports.

· The firm will have to disclose operating data to the public. Many small firms do

not like having to do this, because such information is available to competitors.

Also, some of the firm's officers, directors, and major stockholders will have to

disclose their stock holdings, making it easy for others to estimate their net worth.

· Managers of publicly-owned corporations have a more difficult time engaging in

deals which benefit them personally, such as paying themselves high salaries,

hiring family members, and enjoying not-strictly-necessary, but tax-deductible,

fringe benefits.

· If the company is very small, its stock may not be traded actively and the market

price may not reflect the stock's true value.

The advantages of public ownership would be recognized by key employees, who would most

likely be granted stock options, which would certainly be more valuable if the stock

were publicly traded.

Mini Case: 19 - 400
e. What are the steps of an initial public offering?

20-8 A cancellation clause would reduce the risk to the lessee since the firm would be allowed to terminate

the lease at any point. Since the lease is less risky than a standard financial lease, and less risky than

Answers and Solutions: 20 - 408
straight debt, which cannot usually be prepaid without a prepayment charge, the discount rate on the
cost of leasing might be adjusted to reflect lower risk. (Note that this requires increasing the
discount rate since cash outflows are being discounted.) The effect on the lessor is just the
opposite--risk is increased. (Note that this would also require an increase in the lessor's discount
rate.)

Answers and Solutions: 20 - 409
SOLUTIONS TO END-OF-CHAPTER PROBLEMS

20-1 a. (1) Reynolds' current debt ratio is $400/$800 = 50%.

(2) If the company purchased the equipment its balance sheet would look like:

Current assets $300 Debt (including lease) $600

Fixed assets 500

Leased equipment 200 Equity $400

Total assets $1,000 Total claims
$1,000

Therefore, the company's debt ratio = $600/$1,000 = 60%.

(3) If the company leases the asset and does not capitalize the lease, its debt ratio = $400/$800 =

50%.

b. The company's financial risk (assuming the implied interest rate on the lease is equivalent to the

loan) is no different whether the equipment is leased or purchased.

20-2 Cost of owning:

0 1
2

| | |

Cost (200)

Depreciation shield 40 40

(200) 40 40

PV at 6% = -$127.

Cost of leasing:

0 1
2

| | |

After-tax lease payment (66) (66)

PV at 6% = -$128.

Reynolds should buy the equipment, because the cost of owning is less than the cost of leasing.